Problem: $A$ $B$ $C$ If: $ BC = 6x + 6$, $ AB = 8x + 9$, and $ AC = 141$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 9} + {6x + 6} = {141}$ Combine like terms: $ 14x + 15 = {141}$ Subtract $15$ from both sides: $ 14x = 126$ Divide both sides by $14$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 6({9}) + 6$ Simplify: $ {BC = 54 + 6}$ Simplify to find ${BC}$ : $ {BC = 60}$